LETTER TO THE EDITOR: Transition temperature of the weakly interacting Bose gas: perturbative solution of the crossover equations in the canonical ensemble
Abstract
We compute the shift of the critical temperature T_{c} with respect to the ideal case for a weakly interacting uniform Bose gas. We work in the framework of the canonical ensemble, extending the criterion of condensation provided by the canonical particle counting statistics for the zeromomentum state of the uniform ideal gas. The perturbative solution of the crossover equation to lowest order in powers of the scattering length yields (T_{c}T_{c}^{0})/T_{c}^{0} = 0.93aρ^{1/3}, where T_{c}^{0} is the transition temperature of the corresponding ideal Bose gas, a is the scattering length, and ρ is the particle number density. This result is at variance with the standard grand canonical prediction of a null shift of the critical temperature in the lowest perturbative order. The nonequivalence of statistical ensembles for the ideal Bose gas is thus confirmed (at the lowest perturbative level) also in the presence of interactions.
 Publication:

Journal of Physics B Atomic Molecular Physics
 Pub Date:
 October 2000
 DOI:
 10.1088/09534075/33/20/10j
 arXiv:
 arXiv:condmat/0001422
 Bibcode:
 2000JPhB...33L.779W
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 14 pages (RevTeX)